Stanislav Rokhlin - Academia.edu (original) (raw)
Papers by Stanislav Rokhlin
Journal of Applied Physics, 1986
ABSTRACT An anomalous phenomenon in the reflection and refraction of elastic waves on an interfac... more ABSTRACT An anomalous phenomenon in the reflection and refraction of elastic waves on an interface between anisotropic crystals is analyzed. Due to the deviation of the ray (energy flow) direction from the wave normal for elastic waves in crystals, the domain of permissible incident angles splits into disjoint pieces for certain crystal cuts. This may lead to the existence of grazing angles at three different wave‐vector angles. The grazing angle is defined as the angle at which the ray vector of the incident wave is parallel to the interface. To clarify this interesting phenomenon, numerical calculations were made for the (001) plane of a Ni crystal, based on a calculational procedure developed previously for study of the reflection and refraction of elastic waves in crystals. For each of the two split domains of incident angle there appear two branches of the reflection coefficient for the slow quasi‐transverse wave corresponding to the same slowness surface. The value of the energy conversion of the incident wave into each of these reflected waves depends on the closeness of the direction of the displacement vector in these waves to the incident displacement direction.
Attention is given to two phenomena encountered in the reflection and transmission of ultrasonic ... more Attention is given to two phenomena encountered in the reflection and transmission of ultrasonic waves through an interface between anisotropic materials: (1) the splitting of the domain of incidence angles into disjoint units, in the cases of certain crystal cuts; and (2) the transformation of incident, quasi-longitudinal and quasi-transverse waves into pure shear SH waves. The latter effect may be accounted for by a deviation of the displacement vector of either the incident quasi-longitudinal or quasi-SV waves from the plane of incidence. Both of the effects discussed may substantially complicate the scattering phenomena of ultrasonic waves in polycrystalline materials.
Journal of the Mechanics and Physics of Solids, 2002
In this work, it is suggested that a unique set of the interfacial stiffness constants, K N and K... more In this work, it is suggested that a unique set of the interfacial stiffness constants, K N and K T , is sufficient to characterize the macroscopic elastic response of an interface between two rough contacting surfaces regardless of the direction of incidence of the ultrasonic wave. It is ...
Physical Ultrasonics of Composites
Nondestructive ultrasonic testing of composite materials is affected by several special features ... more Nondestructive ultrasonic testing of composite materials is affected by several special features of wave propagation that arise from the strong anisotropy and inhomogeneity of these materials. The resulting complexity requires re-examination of old testing methodologies and development of new ones. One of the most fundamental phenomena in ultrasonic nondestructive evaluation is the reflection–refraction of ultrasonic waves at a plane interface. Even the simplest test procedure requires understanding of mode conversion and knowledge of elastic wave reflection and transmission coefficients and refraction angles. Reflection–refraction phenomena, while straightforward and well documented for isotropic materials, are much more complicated for anisotropic materials. When analyzing the oblique incidence inspection method for composite materials, one first has to address the problem of wave propagation through the interface between the coupling medium and the composite material. For example...
Physical Ultrasonics of Composites
Composite materials, unless they are quite thin, often include periodic layering, where laminated... more Composite materials, unless they are quite thin, often include periodic layering, where laminated plates composed of alternating uniaxial plies in two or more directions result in more evenly distributed in-plane stiffness. The oriented plies can generally be reduced to a unit cell geometry which repeats throughout the laminate and is composed of sublayers each having highly directional in-plane stiffness, but identical out-of-plane properties. As the transverse isotropy of a uniaxial fibrous ply derives from the geometry of the two-phase material, composite laminates of these plies will have microscopic elastic stiffness tensors which change only in the plane of the laminate, as we saw in Chapter 1. The elastic properties normal to the laminate surface remain unchanged from ply to ply. In this chapter we take up the subject of waves in periodically layered plates. Unusual guided wave dispersion effects have been observed experimentally in periodically layered plates. Shull et al. f...
The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nomi... more The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nominal thickness t form separate, almost spherical magnetic granules of typical diameter 2-3 nm between the Al2O3 spacers, was studied. We discuss measurements of the dc and ac magnetic susceptibility χ for 1 n
Nondestructive Characterization of Materials IV, 1991
Physical Ultrasonics of Composites
Nondestructive ultrasonic testing of composite materials is affected by several special features ... more Nondestructive ultrasonic testing of composite materials is affected by several special features of wave propagation that arise from the strong anisotropy and inhomogeneity of these materials. The resulting complexity requires re-examination of old testing methodologies and development of new ones. One of the most fundamental phenomena in ultrasonic nondestructive evaluation is the reflection–refraction of ultrasonic waves at a plane interface. Even the simplest test procedure requires understanding of mode conversion and knowledge of elastic wave reflection and transmission coefficients and refraction angles. Reflection–refraction phenomena, while straightforward and well documented for isotropic materials, are much more complicated for anisotropic materials. When analyzing the oblique incidence inspection method for composite materials, one first has to address the problem of wave propagation through the interface between the coupling medium and the composite material. For example...
Physical Ultrasonics of Composites, 2011
In the previous chapters, we saw how waves in composites behaved under various circumstances, dep... more In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic...
Physical Ultrasonics of Composites
Composite materials, unless they are quite thin, often include periodic layering, where laminated... more Composite materials, unless they are quite thin, often include periodic layering, where laminated plates composed of alternating uniaxial plies in two or more directions result in more evenly distributed in-plane stiffness. The oriented plies can generally be reduced to a unit cell geometry which repeats throughout the laminate and is composed of sublayers each having highly directional in-plane stiffness, but identical out-of-plane properties. As the transverse isotropy of a uniaxial fibrous ply derives from the geometry of the two-phase material, composite laminates of these plies will have microscopic elastic stiffness tensors which change only in the plane of the laminate, as we saw in Chapter 1. The elastic properties normal to the laminate surface remain unchanged from ply to ply. In this chapter we take up the subject of waves in periodically layered plates. Unusual guided wave dispersion effects have been observed experimentally in periodically layered plates. Shull et al. f...
The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nomi... more The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nominal thickness t form separate, almost spherical magnetic granules of typical diameter 2-3 nm between the Al2O3 spacers, was studied. We discuss measurements of the dc and ac magnetic susceptibility χ for 1 n
Physical Ultrasonics of Composites, 2011
In this chapter we consider elastic wave modes which propagate in composites with finite boundari... more In this chapter we consider elastic wave modes which propagate in composites with finite boundaries. There are those waves that exist between the two plane parallel boundaries of a homogeneous anisotropic solid. We consider that well-known problem, as well as waves in an elastic anisotropic rod, specifically an individual graphite fiber. Composite laminates seen in applications are essentially all multilayered structures, and in many cases can be considered periodically layered. So, we also take up the subject of guided waves in layered plates in later chapters. In a plate geometry, as illustrated in Fig. 5.1, we choose the propagation direction to be parallel to the x1 axis and the x3 axis to be normal to the plate surfaces. This geometry is particularly significant for composite materials since, by design, laminates are often locally planar in nature. While the solutions we find are appropriate for flat plates, with some modifications they describe wave motion in gently curved str...
Nondestructive Characterization of Materials IV, 1991
Physical Ultrasonics of Composites, 2011
In the previous chapters, we saw how waves in composites behaved under various circumstances, dep... more In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic...
Physical Ultrasonics of Composites, 2011
In this chapter we consider elastic wave modes which propagate in composites with finite boundari... more In this chapter we consider elastic wave modes which propagate in composites with finite boundaries. There are those waves that exist between the two plane parallel boundaries of a homogeneous anisotropic solid. We consider that well-known problem, as well as waves in an elastic anisotropic rod, specifically an individual graphite fiber. Composite laminates seen in applications are essentially all multilayered structures, and in many cases can be considered periodically layered. So, we also take up the subject of guided waves in layered plates in later chapters. In a plate geometry, as illustrated in Fig. 5.1, we choose the propagation direction to be parallel to the x1 axis and the x3 axis to be normal to the plate surfaces. This geometry is particularly significant for composite materials since, by design, laminates are often locally planar in nature. While the solutions we find are appropriate for flat plates, with some modifications they describe wave motion in gently curved str...
International Journal of Solids and Structures, 2002
A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavi... more A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavity with two corner cracks is presented. It is applied to determine the depth of the small fatigue cracks initiated from a pit-type surface flaw. The general scattering formalism based on the elastodynamic reciprocity principle is employed. The effect of the cylindrical cavity on the surface wave reflection from cracks is considered using an approximate stress intensity factor for the corner cracks. In situ surface acoustic wave measurements have been performed during fatigue tests for an Al 2024-T3 sample. The surface wave signal was acquired continuously at different cyclic load levels. The model is verified by comparing calculated reflection signals and spectra with those from experiments. The depths of fully and partially open cracks are determined from the predicted and the measured surface wave reflections. The surface wave reflection is observed to be sensitive to crack closure.
International Journal of Solids and Structures, 2002
A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavi... more A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavity with two corner cracks is presented. It is applied to determine the depth of the small fatigue cracks initiated from a pit-type surface flaw. The general scattering formalism based on the elastodynamic reciprocity principle is employed. The effect of the cylindrical cavity on the surface wave reflection from cracks is considered using an approximate stress intensity factor for the corner cracks. In situ surface acoustic wave measurements have been performed during fatigue tests for an Al 2024-T3 sample. The surface wave signal was acquired continuously at different cyclic load levels. The model is verified by comparing calculated reflection signals and spectra with those from experiments. The depths of fully and partially open cracks are determined from the predicted and the measured surface wave reflections. The surface wave reflection is observed to be sensitive to crack closure.
Adhesive Joints, 1984
Methods of measurement of the velocity and attenuation of ultrasonic waves have been used for a l... more Methods of measurement of the velocity and attenuation of ultrasonic waves have been used for a long time for investigating structural and mechanical properties of materials. The main purpose of this article is to show that a properly updated ultrasonic method can be successfully used for investigating surface and interface films, in particular, of adhesively bonded structures. Theoretical analysis of the propagation of elastic waves in a multi-layered medium can be used for relating the velocity of surface and interface waves with the elastic properties of the film and substrates. If the elastic properties of the substrates are known, then the viscoelastic properties of films can be determined from measurements of the velocity and attenuation of these waves. The velocity of surface and interface waves is a function of not only the film properties, but also of adhesion of the film to the substrates. This makes the suggested technique potentially promising for the evaluation of adhesion properties of thin surface and interface films.
Journal of Applied Physics, 1986
ABSTRACT An anomalous phenomenon in the reflection and refraction of elastic waves on an interfac... more ABSTRACT An anomalous phenomenon in the reflection and refraction of elastic waves on an interface between anisotropic crystals is analyzed. Due to the deviation of the ray (energy flow) direction from the wave normal for elastic waves in crystals, the domain of permissible incident angles splits into disjoint pieces for certain crystal cuts. This may lead to the existence of grazing angles at three different wave‐vector angles. The grazing angle is defined as the angle at which the ray vector of the incident wave is parallel to the interface. To clarify this interesting phenomenon, numerical calculations were made for the (001) plane of a Ni crystal, based on a calculational procedure developed previously for study of the reflection and refraction of elastic waves in crystals. For each of the two split domains of incident angle there appear two branches of the reflection coefficient for the slow quasi‐transverse wave corresponding to the same slowness surface. The value of the energy conversion of the incident wave into each of these reflected waves depends on the closeness of the direction of the displacement vector in these waves to the incident displacement direction.
Attention is given to two phenomena encountered in the reflection and transmission of ultrasonic ... more Attention is given to two phenomena encountered in the reflection and transmission of ultrasonic waves through an interface between anisotropic materials: (1) the splitting of the domain of incidence angles into disjoint units, in the cases of certain crystal cuts; and (2) the transformation of incident, quasi-longitudinal and quasi-transverse waves into pure shear SH waves. The latter effect may be accounted for by a deviation of the displacement vector of either the incident quasi-longitudinal or quasi-SV waves from the plane of incidence. Both of the effects discussed may substantially complicate the scattering phenomena of ultrasonic waves in polycrystalline materials.
Journal of the Mechanics and Physics of Solids, 2002
In this work, it is suggested that a unique set of the interfacial stiffness constants, K N and K... more In this work, it is suggested that a unique set of the interfacial stiffness constants, K N and K T , is sufficient to characterize the macroscopic elastic response of an interface between two rough contacting surfaces regardless of the direction of incidence of the ultrasonic wave. It is ...
Physical Ultrasonics of Composites
Nondestructive ultrasonic testing of composite materials is affected by several special features ... more Nondestructive ultrasonic testing of composite materials is affected by several special features of wave propagation that arise from the strong anisotropy and inhomogeneity of these materials. The resulting complexity requires re-examination of old testing methodologies and development of new ones. One of the most fundamental phenomena in ultrasonic nondestructive evaluation is the reflection–refraction of ultrasonic waves at a plane interface. Even the simplest test procedure requires understanding of mode conversion and knowledge of elastic wave reflection and transmission coefficients and refraction angles. Reflection–refraction phenomena, while straightforward and well documented for isotropic materials, are much more complicated for anisotropic materials. When analyzing the oblique incidence inspection method for composite materials, one first has to address the problem of wave propagation through the interface between the coupling medium and the composite material. For example...
Physical Ultrasonics of Composites
Composite materials, unless they are quite thin, often include periodic layering, where laminated... more Composite materials, unless they are quite thin, often include periodic layering, where laminated plates composed of alternating uniaxial plies in two or more directions result in more evenly distributed in-plane stiffness. The oriented plies can generally be reduced to a unit cell geometry which repeats throughout the laminate and is composed of sublayers each having highly directional in-plane stiffness, but identical out-of-plane properties. As the transverse isotropy of a uniaxial fibrous ply derives from the geometry of the two-phase material, composite laminates of these plies will have microscopic elastic stiffness tensors which change only in the plane of the laminate, as we saw in Chapter 1. The elastic properties normal to the laminate surface remain unchanged from ply to ply. In this chapter we take up the subject of waves in periodically layered plates. Unusual guided wave dispersion effects have been observed experimentally in periodically layered plates. Shull et al. f...
The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nomi... more The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nominal thickness t form separate, almost spherical magnetic granules of typical diameter 2-3 nm between the Al2O3 spacers, was studied. We discuss measurements of the dc and ac magnetic susceptibility χ for 1 n
Nondestructive Characterization of Materials IV, 1991
Physical Ultrasonics of Composites
Nondestructive ultrasonic testing of composite materials is affected by several special features ... more Nondestructive ultrasonic testing of composite materials is affected by several special features of wave propagation that arise from the strong anisotropy and inhomogeneity of these materials. The resulting complexity requires re-examination of old testing methodologies and development of new ones. One of the most fundamental phenomena in ultrasonic nondestructive evaluation is the reflection–refraction of ultrasonic waves at a plane interface. Even the simplest test procedure requires understanding of mode conversion and knowledge of elastic wave reflection and transmission coefficients and refraction angles. Reflection–refraction phenomena, while straightforward and well documented for isotropic materials, are much more complicated for anisotropic materials. When analyzing the oblique incidence inspection method for composite materials, one first has to address the problem of wave propagation through the interface between the coupling medium and the composite material. For example...
Physical Ultrasonics of Composites, 2011
In the previous chapters, we saw how waves in composites behaved under various circumstances, dep... more In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic...
Physical Ultrasonics of Composites
Composite materials, unless they are quite thin, often include periodic layering, where laminated... more Composite materials, unless they are quite thin, often include periodic layering, where laminated plates composed of alternating uniaxial plies in two or more directions result in more evenly distributed in-plane stiffness. The oriented plies can generally be reduced to a unit cell geometry which repeats throughout the laminate and is composed of sublayers each having highly directional in-plane stiffness, but identical out-of-plane properties. As the transverse isotropy of a uniaxial fibrous ply derives from the geometry of the two-phase material, composite laminates of these plies will have microscopic elastic stiffness tensors which change only in the plane of the laminate, as we saw in Chapter 1. The elastic properties normal to the laminate surface remain unchanged from ply to ply. In this chapter we take up the subject of waves in periodically layered plates. Unusual guided wave dispersion effects have been observed experimentally in periodically layered plates. Shull et al. f...
The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nomi... more The granular layered magnetic system Co80Fe20(t)/Al2 O3 (3 nm), where the Co80Fe20 layers of nominal thickness t form separate, almost spherical magnetic granules of typical diameter 2-3 nm between the Al2O3 spacers, was studied. We discuss measurements of the dc and ac magnetic susceptibility χ for 1 n
Physical Ultrasonics of Composites, 2011
In this chapter we consider elastic wave modes which propagate in composites with finite boundari... more In this chapter we consider elastic wave modes which propagate in composites with finite boundaries. There are those waves that exist between the two plane parallel boundaries of a homogeneous anisotropic solid. We consider that well-known problem, as well as waves in an elastic anisotropic rod, specifically an individual graphite fiber. Composite laminates seen in applications are essentially all multilayered structures, and in many cases can be considered periodically layered. So, we also take up the subject of guided waves in layered plates in later chapters. In a plate geometry, as illustrated in Fig. 5.1, we choose the propagation direction to be parallel to the x1 axis and the x3 axis to be normal to the plate surfaces. This geometry is particularly significant for composite materials since, by design, laminates are often locally planar in nature. While the solutions we find are appropriate for flat plates, with some modifications they describe wave motion in gently curved str...
Nondestructive Characterization of Materials IV, 1991
Physical Ultrasonics of Composites, 2011
In the previous chapters, we saw how waves in composites behaved under various circumstances, dep... more In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic...
Physical Ultrasonics of Composites, 2011
In this chapter we consider elastic wave modes which propagate in composites with finite boundari... more In this chapter we consider elastic wave modes which propagate in composites with finite boundaries. There are those waves that exist between the two plane parallel boundaries of a homogeneous anisotropic solid. We consider that well-known problem, as well as waves in an elastic anisotropic rod, specifically an individual graphite fiber. Composite laminates seen in applications are essentially all multilayered structures, and in many cases can be considered periodically layered. So, we also take up the subject of guided waves in layered plates in later chapters. In a plate geometry, as illustrated in Fig. 5.1, we choose the propagation direction to be parallel to the x1 axis and the x3 axis to be normal to the plate surfaces. This geometry is particularly significant for composite materials since, by design, laminates are often locally planar in nature. While the solutions we find are appropriate for flat plates, with some modifications they describe wave motion in gently curved str...
International Journal of Solids and Structures, 2002
A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavi... more A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavity with two corner cracks is presented. It is applied to determine the depth of the small fatigue cracks initiated from a pit-type surface flaw. The general scattering formalism based on the elastodynamic reciprocity principle is employed. The effect of the cylindrical cavity on the surface wave reflection from cracks is considered using an approximate stress intensity factor for the corner cracks. In situ surface acoustic wave measurements have been performed during fatigue tests for an Al 2024-T3 sample. The surface wave signal was acquired continuously at different cyclic load levels. The model is verified by comparing calculated reflection signals and spectra with those from experiments. The depths of fully and partially open cracks are determined from the predicted and the measured surface wave reflections. The surface wave reflection is observed to be sensitive to crack closure.
International Journal of Solids and Structures, 2002
A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavi... more A model for the low frequency scattering of a surface acoustic wave by a surface cylindrical cavity with two corner cracks is presented. It is applied to determine the depth of the small fatigue cracks initiated from a pit-type surface flaw. The general scattering formalism based on the elastodynamic reciprocity principle is employed. The effect of the cylindrical cavity on the surface wave reflection from cracks is considered using an approximate stress intensity factor for the corner cracks. In situ surface acoustic wave measurements have been performed during fatigue tests for an Al 2024-T3 sample. The surface wave signal was acquired continuously at different cyclic load levels. The model is verified by comparing calculated reflection signals and spectra with those from experiments. The depths of fully and partially open cracks are determined from the predicted and the measured surface wave reflections. The surface wave reflection is observed to be sensitive to crack closure.
Adhesive Joints, 1984
Methods of measurement of the velocity and attenuation of ultrasonic waves have been used for a l... more Methods of measurement of the velocity and attenuation of ultrasonic waves have been used for a long time for investigating structural and mechanical properties of materials. The main purpose of this article is to show that a properly updated ultrasonic method can be successfully used for investigating surface and interface films, in particular, of adhesively bonded structures. Theoretical analysis of the propagation of elastic waves in a multi-layered medium can be used for relating the velocity of surface and interface waves with the elastic properties of the film and substrates. If the elastic properties of the substrates are known, then the viscoelastic properties of films can be determined from measurements of the velocity and attenuation of these waves. The velocity of surface and interface waves is a function of not only the film properties, but also of adhesion of the film to the substrates. This makes the suggested technique potentially promising for the evaluation of adhesion properties of thin surface and interface films.